Usefulness of Decoherence in Quantum-Walk-Based Hash Function

Abstract

We study the usefulness of the broken-line-type decoherence in quantum Hash functions based on discrete-time quantum walks on a cycle. We first observe that the time-evolution of probability distribution of quantum walks on a cycle is of high sensitivity to such broken-line-type decoherence, increasing with the number of steps in the walk. Based on this observation, we further propose a quantum Hash function based on the broken-line quantum walk on a cycle. Numerical simulation and performance analyses show that decoherence can be useful to improve the performances of quantum hash functions such as better diffusion and confusion, better collision resistance and more uniform distribution of hash values in the hash space. Moreover, our results promote the practical use of quantum-walk-based hash functions in realistic situations.